MATHEMATICS MIDDLE SCHOOL

Three terms of an arithmetic sequence are shown below. Which recursive formula defines the sequence? f(1) = 6, f(4) = 12, f(7) = 18

Answers

Answer 1
Answer:

Answer:

The recursive formula defines the sequence is f(n)=f(n-1)+2.

Step-by-step explanation:

Three terms of an arithmetic sequence are

f(1) = 6

f(4) = 12

f(7) = 18

It means first term is 6, fourth term is 12 and seventh term is 18.

The formula for nth term of an arithmetic sequence is

a_n=a+(n-1)d

where n is number of term, a is first term and d is common difference.

4th term of the AP is

a_n=6+(4-1)d

12=6+3d                  [\because a_4=f(4)=12]

Subtract 6 from both sides.

12-6=3d

6=3d

Divide both sides by 3.

2=d

The common difference is 2.

The recursive formula for an AP is

a_n=a_(n-1)+d

Substitute d=2 in the above equation.

a_n=a_(n-1)+2

It can be written as

f(n)=f(n-1)+2

Therefore the recursive formula defines the sequence is f(n)=f(n-1)+2.
Answer 2
Answer: f(n) = 2(n+2)

can also be written as
f(n) = 2n + 4

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Ryan has 8 kittens. Two are white. Julie has 4 kittens. The fraction of kittens that are not white is the same for Ryan and Julie. What fraction of Julie's kittens are not white? Write in simplest form.

Answers

3/4
Because 6 are not white so 6/8 and divide each by 2
6 divided by 2 = 3
8 divided by 2 = 4
= 3/4

Answer:

1/4 are white. So, 3/4.

Step-by-step explanation:

What percentage is the fraction ‘2/4’ equal to ?A. 30%
B. 20%
C. 50%
D. 40%

Answers

Answer: C.) 50%


Step-by-step explanation:

2/4 simplified = 1/2

1/2 = "one half"

= 50%

The answer is c because 2/4 is 50% of the whole.

Tracy is running in a 5.25km race on Saturday. a marathon is approximately 42km.
how many times as long as Tracy's race is a marathon.

Answers

how amny times more is marathon than tracy's race
tracy t imes x=42
5.25 times x=42
divide both side by 5.25 (since 5.25/5.25=1)
x=8

answe ris 8 times

Answer:

x-8

Step-by-step explanation:

Please help with number 2

Answers

Have you tried Dividing 80 by 15 since that's how he got 10% of 80

Maria is tossing a fair coin. She tosses the coin ten times and it lands on heads eight times. If Maria tosses the coin an eleventh time, what is the probability that it will land on heads?A) 1/5
B) 1/2
C) 4/5
D) 3/2

Answers

The correct answer is B.
The eleventh toss of a coin is independent from previous tosses. So regardless of what happened before, the chance to get heads is always 1/2.

Carol makes 9 and one third cups of snack mix. She puts all of the snack mix into plastic bags. She puts two third cup of the snack mix in each bag. How many plastic bags does Carol need?

Answers

9 1/3 / 2/3
9 1/3 = 28/3
28/3 / 2/3
28/3 x 3/2
84/6
14
she needs 14 bags
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